Ramsey and Nash-Williams combinatorics via Schreier families
Abstract
The main results of this paper (a) extend the finite Ramsey partition theorem, and (b) employ this extension to obtain a stronger form of the infinite Nash-Williams partition theorem, and also a new proof of Ellentuck's, and hence Galvin-Prikry's partition theorem. The proper tool for this unification of the classical partition theorems at a more general and stronger level is the system of Schreier families $({\cal A}_{\xi})$ of finite subsets of the set of natural numbers, defined for every countable ordinal $\xi$.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- April 2004
- DOI:
- 10.48550/arXiv.math/0404014
- arXiv:
- arXiv:math/0404014
- Bibcode:
- 2004math......4014F
- Keywords:
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- Functional Analysis;
- Primary 05D10;
- Secondary 05C55
- E-Print:
- 28 pages, preliminary version